Multiple Fuzzy Soft Sets And Generalized Hesitant Fuzzy Soft Sets And Their Applications In Decision-making

Decision making problems are prevalent and have been playing important roles in real life.In recent years,the theory and method of multiple attribute decision making have been widely studied and applied in medical diagnosis,the economy,engineering management and so on.However,in many practical management decision problems such as the choice of suppliers,the evaluation of project risk,the evaluation of virtual enterprise partner,the selection of outstanding talents,the emergency management,the decision maker often show some degree of hesitation and uncertainty due to the factor limitations such as work experience,thought fuzziness and knowledge level.In order to completely describe the uncertainty information in decision-making system,this thesis introduces the notions of interval-valued multi-fuzzy soft sets,possibility interval-valued multi-fuzzy soft sets and generalized hesitant fuzzy soft sets to describe the multi-fuzzy degree,possibility degree and hesitation degree in the evaluation of alternatives,respectively.Based on the existing research,this thesis explores some basis operations and properties of the interval-valued multi-fuzzy soft sets,possibility interval-valued multi-fuzzy soft sets and generalized hesitant fuzzy soft sets,and investigates decision making methods under these fuzzy uncertain environments.The results obtained are as follows:(1)Interval-valued multi-fuzzy soft sets and its algebraic properties research.Combining interval-valued fuzzy sets with multi-fuzzy soft sets,this thesis puts forward the concept of interval-valued multi-fuzzy soft set by using interval number to express the multi-fuzzy degree of an element belonging to a given set.Based on the union and intersection operations on interval numbers,the thesis defines the union and intersection operations on interval-valued multi-fuzzy soft sets,studies the basis properties of interval-valued multi-fuzzy soft sets such as commutative law,associative law,absorption law,distributive law and De Morgan's law,and approves the conclusion that all the interval-valued multi-fuzzy soft sets with union and intersection operators turn out to be a distributive lattice.(2)Possibility interval-valued multi-fuzzy soft sets and its decision making method research.By using interval number to express the degree of multi-fuzzy and possibility of an element belonging to a given set,this thesis puts forward the concept of possibility interval-valued multi-fuzzy soft set.The thesis defines the operations on possibility interval-valued multi-fuzzy soft sets such as the union,intersection and complement,and studies the algebraic properties that possibility interval-valued multi-fuzzy soft sets satisfy the commutative,associative,absorption,distributive and De Morgan's law and so on.It is shown that the algebraic system consisting of all the possibility interval-valued multi-fuzzy soft sets with union and intersection operators turns out to be a distributive lattice.Also,the thesis puts forward the multiple attribute group decision making method in possibility interval-valued multi-fuzzy soft sets environment.Moreover,the case analysis for the best manager selection validates the approach in decision making.(3)The algebraic properties of generalized hesitant fuzzy soft sets and its decision making method research.Based on the union,intersection,strict union and strict intersection operations on hesitant fuzzy elements,this thesis proposes the notions of generalized union,generalized intersection,generalized strict union,generalized strict intersection,narrow union,narrow intersection,narrow strict union and narrow strict intersection operations,studies the basic properties such as the commutative,associative,absorption,distributive and De Morgan's law of generalized hesitant fuzzy soft sets,and investigates the algebraic structure of generalized hesitant fuzzy soft sets with these operations.In particular,the algebraic system consisting of all the generalized hesitant fuzzy soft sets with narrow strict union and generalized strict intersection operators constitutes a lattice.Based on the generalized comparison table,this thesis presents the possibility degree formula of the proposition that one object is not superior to another object,and proposes the multiple attribute decision making method based on generalized hesitant fuzzy soft sets.Moreover,this thesis explores the decision making method to handle the selection of campus outstanding student and purchase of optimal house.It is shown that the proposed method is feasible and effective in decision making problems.